How do I delete edges inside my model?
You could select the verts that are connected to these edges and then hit X >> 'Edges'. But Edge Select Mode is much better for this. You can change the select mode in the header:



Now you can simply right click them and delete them.

The faster way that might work:

In Edge Select Mode, deselect everything with A, then hit CTRLALTSHIFTM. This will select all edges that do not have 2 faces attached to them. 

But your Mesh has a Mirror Modifier, so you'd have to deselect those edges. Luckily there's a third option:

Be in Edge Select Mode, select one of these edges with a right click and then choose from the header menu:

'Select' >> 'Select similar' >> 'Amount of faces around an Edge'. All orphan edges will be selected and you can hit x >> 'Edges'.